Problem: Simplify the following expression: $p = \dfrac{q^2 - q - 72}{q + 8} $
Answer: First factor the polynomial in the numerator. $ q^2 - q - 72 = (q + 8)(q - 9) $ So we can rewrite the expression as: $p = \dfrac{(q + 8)(q - 9)}{q + 8} $ We can divide the numerator and denominator by $(q + 8)$ on condition that $q \neq -8$ Therefore $p = q - 9; q \neq -8$